/C

# ccoshf, ccosh, ccoshl

Defined in header `<complex.h>`
`float complex       ccoshf( float complex z );`
(1) (since C99)
`double complex      ccosh( double complex z );`
(2) (since C99)
`long double complex ccoshl( long double complex z );`
(3) (since C99)
Defined in header `<tgmath.h>`
`#define cosh( z )`
(4) (since C99)
1-3) Computes the complex hyperbolic cosine of `z`.
4) Type-generic macro: If `z` has type `long double complex`, `ccoshl` is called. if `z` has type `double complex`, `ccosh` is called, if `z` has type `float complex`, `ccoshf` is called. If `z` is real or integer, then the macro invokes the corresponding real function (`coshf`, `cosh`, `coshl`). If `z` is imaginary, then the macro invokes the corresponding real version of the function `cos`, implementing the formula cosh(iy) = cos(y), and the return type is real.

### Parameters

 z - complex argument

### Return value

If no errors occur, complex hyperbolic cosine of `z` is returned.

### Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

• `ccosh(conj(z)) == conj(ccosh(z))`
• `ccosh(z) == ccosh(-z)`
• If `z` is `+0+0i`, the result is `1+0i`
• If `z` is `+0+∞i`, the result is `NaN±0i` (the sign of the imaginary part is unspecified) and `FE_INVALID` is raised
• If `z` is `+0+NaNi`, the result is `NaN±0i` (the sign of the imaginary part is unspecified)
• If `z` is `x+∞i` (for any finite non-zero x), the result is `NaN+NaNi` and `FE_INVALID` is raised
• If `z` is `x+NaNi` (for any finite non-zero x), the result is `NaN+NaNi` and `FE_INVALID` may be raised
• If `z` is `+∞+0i`, the result is `+∞+0i`
• If `z` is `+∞+yi` (for any finite non-zero y), the result is `+∞cis(y)`
• If `z` is `+∞+∞i`, the result is `±∞+NaNi` (the sign of the real part is unspecified) and `FE_INVALID` is raised
• If `z` is `+∞+NaN`, the result is `+∞+NaN`
• If `z` is `NaN+0i`, the result is `NaN±0i` (the sign of the imaginary part is unspecified)
• If `z` is `NaN+yi` (for any finite non-zero y), the result is `NaN+NaNi` and `FE_INVALID` may be raised
• If `z` is `NaN+NaNi`, the result is `NaN+NaNi`

where cis(y) is cos(y) + i sin(y).

Mathematical definition of hyperbolic cosine is cosh z = ez+e-z/2

Hyperbolic cosine is an entire function in the complex plane and has no branch cuts. It is periodic with respect to the imaginary component, with period 2πi.

### Example

```#include <stdio.h>
#include <math.h>
#include <complex.h>

int main(void)
{
double complex z = ccosh(1);  // behaves like real cosh along the real line
printf("cosh(1+0i) = %f%+fi (cosh(1)=%f)\n", creal(z), cimag(z), cosh(1));

double complex z2 = ccosh(I); // behaves like real cosine along the imaginary line
printf("cosh(0+1i) = %f%+fi ( cos(1)=%f)\n", creal(z2), cimag(z2), cos(1));
}```

Output:

```cosh(1+0i) = 1.543081+0.000000i (cosh(1)=1.543081)
cosh(0+1i) = 0.540302+0.000000i ( cos(1)=0.540302)```
• C11 standard (ISO/IEC 9899:2011):
• 7.3.6.4 The ccosh functions (p: 193)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• G.6.2.4 The ccosh functions (p: 541)
• G.7 Type-generic math <tgmath.h> (p: 545)
• C99 standard (ISO/IEC 9899:1999):
• 7.3.6.4 The ccosh functions (p: 175)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• G.6.2.4 The ccosh functions (p: 476)
• G.7 Type-generic math <tgmath.h> (p: 480)

 csinhcsinhfcsinhl (C99)(C99)(C99) computes the complex hyperbolic sine (function) ctanhctanhfctanhl (C99)(C99)(C99) computes the complex hyperbolic tangent (function) cacoshcacoshfcacoshl (C99)(C99)(C99) computes the complex arc hyperbolic cosine (function) coshcoshfcoshl (C99)(C99) computes hyperbolic cosine (\({\small\cosh{x} }\)cosh(x)) (function) C++ documentation for `cosh`